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On a Babuška Paradox for Polyharmonic Operators: Spectral Stability and Boundary Homogenization for Intermediate Problems

  • Francesco FerraressoEmail author
  • Pier Domenico Lamberti
Article

Abstract

We analyse the spectral convergence of high order elliptic differential operators subject to singular domain perturbations and homogeneous boundary conditions of intermediate type. We identify sharp assumptions on the domain perturbations improving, in the case of polyharmonic operators of higher order, conditions known to be sharp in the case of fourth order operators. The optimality is proved by analysing in detail a boundary homogenization problem, which provides a smooth version of a polyharmonic Babuška paradox.

Keywords

Spectral analysis Polyharmonic operators Boundary homogenization 

Notes

Acknowledgements

The authors are deeply indebted to Prof. J.M. Arrieta for valuable suggestions and discussions. The first author gratefully acknowledges the support of the Swiss National Science Foundation, SNF, through the Grant No. 169104. The second author acknowledges financial support from the INDAM - GNAMPA project 2017 “Equazioni alle derivate parziali non lineari e disuguaglianze funzionali: aspetti geometrici ed analitici” and the INDAM - GNAMPA project 2019 “Analisi spettrale per operatori ellittici con condizioni di Steklov o parzialmente incernierate”. The authors are also members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Copyright information

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Authors and Affiliations

  1. 1.Institute of MathematicsUniversität BernBernSwitzerland
  2. 2.Dipartimento di Matematica “Tullio Levi-Civita”Università degli Studi di PadovaPaduaItaly

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